Miscible fingering in electrokinetic flow

Analysis is carried out to examine the miscible fingering phenomenon when a fluid with a lower electrolyte concentration advances into one with a higher concentration. Unlike earlier miscible fingering theories, the linear stability analysis is carried out in the self-similar coordinates of the diffusing front. The dominant destabilizing mode is shown to be a localized concentration disturbance within the diffusive layer. However, transverse diffusion is shown to eventually stabilize the instability at time t=t_c that scales as b^8/3 where b is the breadth of the channel, and lengthen the dominant transverse wavelength as t^3/8 in the interim. With these scaling laws, we arrive at the conclusion that transient fingering is insignificant in sub-millimeter micro-devices which use electrokinetic flow to transport biological and environmental electrolyte samples.